In dynamic collective decision making, current decisions determine the future distribution of political power and influence future decisions. We develop a general framework to study this class of problems. Under acyclicity, we characterize dynamically stable states as functions of the initial state and obtain two general insights. First, a social arrangement is made stable by the instability of alternative arrangements that are preferred by sufficiently powerful groups. Second, efficiency-enhancing changes may be resisted because of further changes they will engender. We use this framework to analyze dynamics of political rights in a society with different types of extremist views. (JEL D71, D72, K10)